Data Analysis with Microsoft Excel: Updated for Office 2007

328 Statistical Methods

hypothesis that a linear relationship exists between the mortality index and

temperature. On the basis of the confi dence interval for the slope param-

eter, you can report with 95% confi dence that for each degree increase in

the mean annual temperature, the mortality index for the region increases

between 1.61 to 3.11 points.

Residuals and Predicted Values

The last part of the output from the Analysis ToolPak’s Regression command

consists of the residuals and the predicted values. See Figure 8-13 (the values

have been reformatted to make them easier to view).

Figure 8-13
Residuals
and predicted
values

As you’ve learned, the residuals are the differences between the observed

values and the regression line (the predicted values). Also included in the

output are the standardized residuals. From the values shown in Figure 8-13,

you see that there is one residual that seems larger than the others, it is found

in the fi rst observation and has a standardized residual value of 1.937. Stan-

dardized residuals are residuals standardized to a common scale, regardless

of the original unit of measurement. A standardized residual whose value is

above 2 or below 22 is a potential outlier. There are many ways to calculate

standardized residuals. Excel calculates using the following formula:

Standardized residual 5

Residual

"Sum of squared residuals@^1 n 212

where n is the number of observations in the data set. In this data set, the

value of the fi rst standardized residual is

14. 12
    "796.9058@ 15

5 1.937

You’ll want to keep an eye on this observation as you continue to explore

this regression model. As you’ll see shortly, the residuals play an important

role in determining the appropriateness of the regression model.